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D.1. TUTORIAL 1: Anchored diaphragm wall

The following example is based on an paper written by D. Gouvenot et M. Bustamante in Annales de lInstitut Technique du Btiment et des Travaux Publics n 375, published in September 1979. This tutorial deals with the design of an anchored diaphragm wall on the building site of the Gravelines nuclear plant (France). It's the retaining wall along the bank of water supply canal. The geological configuration is that of a typical shoreline. The objective of this tutorial is to show the basic functions of K-REA throughout the study of this example: Step 1: Data input Step 2: Staged construction, and calculation Step 3: Results display

> Sign pointing out the data required for the tutorial.

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D.1.1. STEP 1: DATA INPUT

Launch K-REA by clicking Start, Programs, and K-REA. Choose your language, then the local or network mode. Select New Project. The main options of this project should now be defined. D.1.1.1. TITLE AND OPTIONS Select the Data menu, choose Title and Options.

The Title and Options dialogue box appears as shown:

Fill in this dialogue box with the required project options. > To go on with Tutorial 1: select the white Title empty box and type in your own title; do so to enter the project number;

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keep the default units system, kN, kPa, m, and the water weight 10 kN/m3 as shown above; keep the Definition of the project in depths, which will define a positive depth scale oriented downwards; in the Calculation options dialogue box, keep all the default values (10 iterations per phase and a calculation step of 0,5 m); do not check the Output display option; finally, click on Validate and Quit.

Save the new project in the proper directory by selecting the File menu then Save. D.1.1.2. SOIL PROPERTIES Select the Data menu, choose Soil layers.

Data display table

Data input zone

> To go on with Tutorial 1: o o In the data display table, select the first soil layer. In the data input dialogue box, enter the soil properties as defined in the following table.

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o o

Click on the number of the next layer in the summary table to switch to the next layer which should be defined. Click Validate and Quit when all the soil layers have been defined (but first click once in the upper table).

a/ 0.66 0.66 0.66 0.66 0.66

p/ -0.66 -0.66 -0.66 -0.66 -0.66

kh (kN/m3) 20000 50000 30000 50000 100000

dkh (kN/m3/m) 0 0 0 0 0

0.260 0.282 0.529 0.227 0.282

Note: The soil properties and the values for the subgrade reaction coefficient are defined according to the paper mentioned in the introduction. The earth pressure coefficients ka et kp have been read in the Krisel and Absi tables, with =0, =0 and

2 = . 3

k0 has been calculated using the Jaky formula; k 0 = 1 sin except for the black clay layer. The coefficients applied to the cohesion have been calculated using the Caquot formulae (given par the specific wizard). The k0 Jaky, ka/kp (Krisel & Absi), kd=k0, kr=k0 and ca/cp wizards have been used to fill in the properties. The use of the various wizards is detailed in tutorial 2.

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> To go on with Tutorial 1: o o Choose the product of inertia definition mode by checking the appropriate radio button. Then select the first line of the empty table to define the wall properties, and the empty box below the table to fill in the bottom level for the wall:Head level (m) Bottom level (m) EI Product (kN.m2)

Retaining wall

21.5

500000

Note: in that example, all the data are defined per linear meter. To change the working width L for the retaining wall, use the advanced properties.

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D.1.2. STEP 2: DEFINITION OF STAGES AND ACTIONS

After completion of the previous step, the screen appears as shown:

Actions selection zone

Action parameters zone

Phase management zone

Here should be defined all actions used in the initial phase, but our example uses none. We shall thus create a first calculation phase. Note 1: the downhill side is always on the left of the wall, which means that all anchors will be located in the soil to the right of the wall and all struts will be located on the left to the wall. The uphill side is on the right side of the wall. Note 2: displacements and forces are positive if the wall moves from the left to the right. Moments are positive anti-clockwise. The complete staged construction for this example is described in the next table. It is a succession of excavations (with variations of the groundwater level) and anchors installations (3 levels of anchors). Note: The Excavation-Water action actually consists in 3 actions. It can be used not only to define the earthwork, but also the changes in the water level (as shown in the example) and a distributed surcharge applied to the groundlevel on one side of the wall.

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Actions Initial phase Phase 1 Excavation-Water (excavation downhill to 3.7 m and water level at 15.2 m) Anchors (installation of an anchor at 3.2 m) Excavation-Water (excavation down to 8.2 m) Anchors (installation of an anchor at 7.7 m) Excavation-Water (excavation down to 12.5 m) Anchors (installation of an anchor at 12.2 m) Excavation-Water (excavation down to 14.7 m) Excavation-Water (rise of the water level downhill to 8.2 m) Excavation-Water (rise of the water level downhill and uphill to 2.2 m)

Excavation-Water (drawdown to 8.2 m)

Excavation-Water (rise of the water level downhill to 0.2 m)

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D.1.2.1. DEFINITION OF STAGE N 1 To start the staged construction definition, a new phase should be created. Click on in the phase management zone.

A new tab appears with the schematic initial profile of the soil. Now choose the action to be executed during phase 1 in the actions selection zone. Choose Earthworks then select Excavation-Water. Click on the transfer button .

You can now launch a first calculation if you click on

After the calculation in phase 1, the main window should look like that:

Actions, results and graphics zone

Excavation-Water parameters zone

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One may notice that the parameters zone still displays the parameters input for the Excavation-Water action (excavation 3.7 m deep and groundwater level at 15.2 with no surcharge). One may as well notice the modification of the soil profile in the upper left zone, and the curves summarizing the calculation results. D.1.2.2. DEFINITION OF THE FOLLOWING STAGES To add another phase, click on and proceed as described above.

A new tab appears with the profile of the soil after completion of phase 1. An action type should now be selected for phase 2. To go on with tutorial 1, select Anchors-Wall then Anchors in the appropriate menu. Click on the transfer button .

After completion of phase 2, the interface appears as shown below:

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To go on with tutorial 1, repeat all the operations described in the table page 8, until all 11 stages have been defined. To launch the calculation for all the stages, click on .

After calculation, the main results are displayed in the main window (inside the phase management zone). The tabs named after the corresponding phases make browsing between all different phases and results quite convenient. Curves are displayed with the same scale if the same scale for curve option was checked in the Data/Title and Options dialogue box.

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D.1.3. STEP 3: RESULTS DISPLAY

K-REA allows the complete results to be displayed in a specific window, as curves or tables. Select the Calculation/Results menu then choose Results:

or directly click on the button

A specific window shows up. It presents all the data and results of the project. All the general data can be found under the Data tab: a reminder for the units system chosen, the water weight, the soil layers, and the wall properties, as well as the options checked in the initial phase.

The different Phase tabs (in the Table visualisation mode) show the numerical results in a table. Reminders of the action parameters are displayed below the tables.

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The Results synthesis tab summarises the results: wall displacements, shear forces and moments in the wall, and forces in anchors.

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The last tab (Envelope) shows up the envelope curves for displacements, shear forces and moments. In this example, we didn't request anything special, so the envelope is automatically calculated for all phases (1 to 11).

Two buttons are always available in the Results window: Quit (to close the Results window), and Print (which calls up the printing wizard).

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D.1.4. STEP 4: WORKING WITH A DIFFERENT WALL WIDTH (ALTERNATIVE)

First "save as" the project with a different filename (to avoid overwriting the previous calculation). To do so, select the File menu, and then choose Save as. We will now study the wall with a different working width (the working width was previously equal to one linear meter, as nothing else had been specified). The new working width will be equal to 2.8 m (horizontal spacing between the different anchors in layers 1 and 2. Note: in layer 3, the horizontal spacing between anchors is 1.4 m). Select Data, then Retaining wall. Check the Advanced properties box. Click in L column on line 1 and replace the default value 1m with 2.8m. Click in EI column on line 1 and change the value from 500 000 to 1 400 000 kN.m2 (EI value should be provided for the working width).

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After changing these values, a new calculation can be run. All results are then proportional to the new work width (2.8 m):

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Note: the values of moments and shear forces in the wall depend on the width of the wall L. The values of forces in the anchors and struts depend on the width of the wall L and on the anchors horizontal spacing eh. To get the forces per anchor, the values provided by the software should be multiplied by (eh/L). Consequently, if you input L=eh, the forces calculated by K-REA are directly those per anchor.

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D.2. TUTORIAL 2: Soldier-pile wall with 2 struts levels

D.2.1. PRESENTATION OF THE PROJECTThis example deals with a soldier-pile wall. Lateral earth pressures should be reduced in the initial phase. Anchors are struts. This example illustrates the use of the three different types of excavations available in K-REA: simple excavation, excavation with berm, and excavation with sheeting. The geological cross-section is composed of three soil layers.

D.2.2. STEP 1: DATA INPUT

D.2.2.1. TITLE AND OPTIONS o o o Launch K-REA using the Start menu in Windows. Select "English" and the appropriate mode (local, network or demo). Select New project. Select the Data menu, then Title and Options.

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o o o o o o o

In the Title / N of the project, click in the empty Title box and type in the title you chose for the project. Type in the project number. Choose the appropriate units system (here kN, kPa, m) by checking the corresponding box. The water weight can be changed from 10 kN/m3 (default value) to 9.81 kN/m3. Choose a Definition of the project in Levels, which will define a positive axis oriented upwards. In the Calculation options zone, keep the default values (10 iterations per phase and a calculation step of 0.5 m for the wall). Finally, check the box Display ratio limiting/mobilised earth resistance.

The following window is displayed:

o o

Click Validate and Quit. Save the new project in the proper directory by selecting the File menu then Save.

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The properties for the 3 soil layers should be input. o Fill in the properties of the first soil layer. The first line of the summary table has already been selected by K-REA. Click in the first box under the table, after Name: and enter the name of the first soil layer (here Layer 1). Then select the box Top level Zl and type in the top level for the first layer (here 174 m). Do the same to enter PVh, PVd, , c, dc, a/ and p/, the values of which are shown in the table below: Name Layer 1 Top Zl Zwater PVh PVd (m) (kN/m3) (kN/m3) 174 164 20 10 () 15 c dc (kPa) (kPa) 5 0 a/ p/

o o

0.00 -0.66

!!!! Beware with the format of a/ and p/. Those values will automatically be used by the wizards !!!! o To fill in the k0 box, click on the Jaky wizard button. This wizard calculates k0 using the value of the friction angle and the k0 = 1-sin formula.

This is what should be displayed:

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To input ka, click on the ka/kp wizard button on the right. Choose the tables for passive and active earth pressures by Krisel and Absi (click on OK in the dialogue box). Select the table you want to display by selecting "Active pressure" in the upper-right list. The following screenshot illustrates that procedure:

The internal friction angle is automatically set by K-REA to the value that you previously defined (here 15) and the angle between the wall and the vertical is always set to 0. But you need to fill in the angle between the groundlevel and the horizontal. To do so, click 0 in the / menu. Then click on the Transfer >> button to transfer the value of ka. Click once again in the upper menu and select the Passive pressure table type:

o o o

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Transfer the value using the Transfer >> button and Click on Quit to get out of the wizard. Resume the definition of Layer 1. o o o o To fill in kd and kr, click on the k0 automatic wizards. These wizards fill in kd and kr with k0 value (here 0.741). To fill in ca and cp, click on the ca/cp wizard. The internal friction angles as well as the obliquities are automatically filled in. Click on Transfer >> and then on Quit. The only parameter left is kh. Click in the kh box and enter 14,000 kN/m3. Click in the dkh box and type in 0.

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D.2.2.3. WALL PROPERTIES The wall in this example extends from level 157 m to the groundlevel. It is composed of concrete circular piles with a 30 GPa Youngs modulus, and 0.45m diameter. Their horizontal spacing is 2.25 m. o o o Select the Data menu then Retaining wall. Choose the product of inertia definition mode by checking the appropriate box. First click EI column on line 1, then click on the Wizard button to calculate the product of inertia EI of the concrete piles. Choose "spaced or jointed circular piles". Define the Youngs modulus (30 GPa) for the piles, their horizontal spacing (2.25m) and their diameter (0.45 m). Click on Transfer then exit the wizard.

!!!! If you click Quit and Save in the retaining wall wizard, the input data will be saved and displayed again next time you open the same wizard !!!! o o Click in Z column on line 1 in the data input table. Fill in the value for Z = top of the wall (here 174). Click in the Zb box to define the bottom level of the wall (here 157).

The screenshot below shows the dialogue box with the data:

Finally, click on Validate and Quit to save the data and have the displayed on the schematic profile in the main window. Save all data.

Note: in this example, the data are input per linear metre.

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D.2.3. STEP 2: DEFINITION OF THE CALCULATION PHASES

After completion of step 1, the screen should look like that:

The main window of K-REA shows the initial phase of the project, with the schematic profile of the soil layers and the wall. The phases should now be defined. Each phase includes one or several actions: PHASE Initial 1 ACTIONS Caquot surcharge of 30 kPa on the horizontal ground surface Reduced pressure on the wall (0.2 active and 0.4 passive) Excavation down to 172 m (downhill side) Excavation with berm down to 170 m (berm head is 5m wide and bottom is 8m wide), downhill side Installation of a strut at level 173 m. Strut stiffness is 50000 kN/m Excavation and sheeting down to 169 m (downhill side) Installation of a strut at level 169 m. Strut stiffness is 50000 kN/m Excavation and sheeting down to 165 m (downhill side)

2 3

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D.2.3.1. INITIAL PHASE next to the The first action is the Caquot surcharge: just click on the transfer button initial phase menu. The keyword Caquot surcharge should appear in the list of actions on the right and the corresponding action parameter zone should appear right under the list of actions. Input the value of the surcharge (30 kPa):

Click on project:

. This action should become visible on the schematic profile of the

Repeat the same operations to apply a reduced pressure. Select Reduced pressure in the . The corresponding keyword initial phase action menu. Click on the transfer button appears in the list of applied actions on the right. All actions in that list are considered by K-REA as an immediate sequence. Fill in the parameters of the selected action (z1=174, z2=157, R=0.2 and C=2). There is no graphical display for this action on the schematic profile, but do not omit to validate it, otherwise the corresponding data will never be saved.

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All actions in the initial phase have been defined. Let us switch to phase 1. in the staged construction management zone. A To create a new phase, click on new tab appears, and the list of actions on the right is empty for this new stage.

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D.2.3.2. PHASE 1 To begin with the actions in phase 1, the first one being a simple excavation, click on the next to the Excavation-Water action in the action selection zone. The transfer button corresponding keyword appears in the list of selected actions. Fill in the parameters for the excavation: downhill side, z=172, z1=164, S=0. The main excavation in K-REA is always located on the left side of the wall (downhill side). K-REA allows to define a simple excavation, a groundwater level variation and a Caquot surcharge all in one action. Therefore the changes "excavation down to 172 m" and "water level maintained at 164 m" can be defined simultaneously using the Excavation-Water action. Note: even if the waterlevel (Zwater ) does not change during the project and if there is no Caquot surcharge applied at excavation level, you need to fill in z1=Zwater and S=0 for each Excavation-Water action.

Click on

The second action in the first phase is a berm. A berm action should always be defined right after an Excavation-Water action, because the Excavation-Water action is used to provide the top level of the berm.

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Click on the Earthworks menu in the action selection zone. Select the berm action, then the transfer button . Fill in the parameters for the berm action (z=170 m for the bottom level, a=5 m and b=8 m).

Click on

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D.2.3.3. PHASE 2 next The first action of phase 2 is the installation of a strut. Click on the transfer button to the Strut action in the action selection zone (in the "anchors-wall" menu). The corresponding keyword appears in the list of selected actions. Fill in the parameters for the strut, in the action parameters zone (activate a new anchor, z=173 m and K=50,000 kN/m).

Click on

The second action in phase 2 is an excavation with sheeting. To define it, two different actions should be used: first an Excavation-Water action, then a Sheeting installation action. Create an Excavation-Water action and define it with: downhill side, excavation level z=169, waterlevel z1=164 and surcharge S=0. Create a Sheeting installation action and define it with: sheeting bottom level = 169 m.

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Click on

The right-click menu on the schematic profile allows to display the properties of the soil layers, anchors, etc. For example, top levels for soil layers and layer names can be displayed:

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D.2.3.4. PHASE 3 Using the example above (definition of phase 2), define for phase 3 a strut at level z=169 m, with a stiffness K=50,000 kN/m, and then an excavation with sheeting down to level z=165 m.

D.2.4. STEP 3: CALCULATION AND RESULTS

After completion of step 2, click on to perform the calculation for all stages.

Note: the calculation can be asked for at any time, as long as parameters of the project, soil layers and wall are saved (Data menu filled in). The curves for displacements, moments and shear forces are displayed in the current phase tab. To view all detailed results in K-REA, click on The following window shows up: .

It shows all the data calculated by K-REA: The Data tab displays all the project data, the units system, the water weight, the properties of the soil layers and the wall, as well as the options chosen during the initial phase, etc. The Phases tabs display all the results described in part B of this manual, chapter B.5.2. Results. Each tab allows both for curves and tables display. The Envelope tab displays the envelope curves.

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The screenshot below illustrates the envelope curves calculated at the end of this example:

The printing wizard on each tab allows to select the data and results you wish to print (see also part B, chapter B.8. Printing).

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D.3. TUTORIAL 3: Anchored diaphragm wall in soft soils

D.3.1. PRESENTATION OF THE PROJECTThis example of a diaphragm wall in Bangkok clays demonstrates the importance and influence of unloading and reloading coefficients. This tutorial is less detailed than the previous ones, but it points out specific functionalities of the K-REA calculation engine.

D.3.2. STEP 1: DATA INPUT

D.3.2.1. TITLE AND OPTIONS In this example, the project is defined using levels and all other parameters will keep their default values. The following screenshot shows the Title and Options dialogue box:

D.3.2.2. SOIL PROPERTIES Select the Data menu, then Soil layers. All properties for the three soil layers should be input. There are three different layers of clays. In the first layer of soft clay, the cohesion and subgrade reaction coefficient increase with depth. The values of plastic earth pressures are defined by:

For all layers, k0 has been calculated using the Jaky formula. !!! The other wizards have not been used to enter the data. Each box can actually be filled in without using the wizards. Wizards are only a help to the user, they are not a compulsory step !!! The following screenshot gives an overview of the three layers:

D.3.3. STEP 2: DEFINITION OF THE CALCULATION PHASES

This example deals with an anchored excavation. The staged construction is divided into series of excavations and anchors installations. A hydraulic gradient is applied all along the project in order to take into account the impermeable layer, between 16 and 20 m under the groundlevel.

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PHASE Initial 1

ACTIONS Hydraulic gradient both on downhill and uphill sides from -16 m to -17 m, in order to simulate the initial state of water pressures along the first meter of the impermeable layer Excavation downto -1.6 m (downhill side) Drawdown of the water to -1.6 m (downhill side) Hydraulic gradient (downhill side) to keep the distribution of water pressures Installation of a horizontal anchor at -1.35 m, with a stiffness of 50,000 kN/m, a prestress force of 100 kN Excavation downto -5.2 m (downhill side) Drawdown of the water to -5.2 m (downhill side) Hydraulic gradient (downhill side) Installation of a horizontal anchor at -4.85 m. Its stiffness is 50,000 kN/m, and its prestress force 150 kN Excavation downto -7.6 m (downhill side) Drawdown of the water to -7.6 m (downhill side) Hydraulic gradient (downhill side) Installation of a horizontal anchor at -7.35 m. Its stiffness is 50,000 kN/m, and its prestress force 200 kN. Excavation downto -10.1 m (downhill side) Drawdown of the water to -10.1 m (downhill side) Hydraulic gradient (downhill side) Installation of a horizontal anchor at -9.85 m. Its stiffness is 50,000 kN/m, and its prestress force 250 kN Excavation downto -15.5 m (downhill side) Drawdown of the water to -15.5 m (downhill side) Hydraulic gradient (downhill side)

3 4

5 6

7 8

9 10

Note: horizontal anchors simulate prestressed struts. These prestressed struts could also have been defined in K-REA by anchors with a zero stiffness plus struts with a stiffness equal to that of the former anchors (50,000 kN/m). This is made possible in K-REA thanks to the superposition of anchors on a same point. The following pages show a summary of all these actions:

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D.3.4. STEP 3: RESULTS DISPLAY

The screenshots thereafter show the results of the calculation for phase 10 as well as the envelope curves:

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It is also possible to view a synthesis of the results, that shows the maximal forces in the wall and the forces calculated in the anchors (screenshot below).